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Properties

Modulus 731025731025
Structure C2×C18×C10260C_{2}\times C_{18}\times C_{10260}
Order 369360369360

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(731025)
 
pari: g = idealstar(,731025,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 369360
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C18×C10260C_{2}\times C_{18}\times C_{10260}
sage: H.gens()
 
pari: g.gen
 
Generators = χ731025(279776,⋅)\chi_{731025}(279776,\cdot), χ731025(321652,⋅)\chi_{731025}(321652,\cdot), χ731025(129601,⋅)\chi_{731025}(129601,\cdot)

First 32 of 369360 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character Orbit Order Primitive −1-1 11 22 44 77 88 1111 1313 1414 1616 1717 2222
χ731025(1,⋅)\chi_{731025}(1,\cdot) 731025.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ731025(2,⋅)\chi_{731025}(2,\cdot) 731025.bvw 10260 yes −1-1 11 e(73310260)e\left(\frac{733}{10260}\right) e(7335130)e\left(\frac{733}{5130}\right) e(20212052)e\left(\frac{2021}{2052}\right) e(7333420)e\left(\frac{733}{3420}\right) e(17395130)e\left(\frac{1739}{5130}\right) e(61710260)e\left(\frac{617}{10260}\right) e(2895130)e\left(\frac{289}{5130}\right) e(7332565)e\left(\frac{733}{2565}\right) e(10511140)e\left(\frac{1051}{1140}\right) e(421110260)e\left(\frac{4211}{10260}\right)
χ731025(4,⋅)\chi_{731025}(4,\cdot) 731025.bug 5130 yes 11 11 e(7335130)e\left(\frac{733}{5130}\right) e(7332565)e\left(\frac{733}{2565}\right) e(9951026)e\left(\frac{995}{1026}\right) e(7331710)e\left(\frac{733}{1710}\right) e(17392565)e\left(\frac{1739}{2565}\right) e(6175130)e\left(\frac{617}{5130}\right) e(2892565)e\left(\frac{289}{2565}\right) e(14662565)e\left(\frac{1466}{2565}\right) e(481570)e\left(\frac{481}{570}\right) e(42115130)e\left(\frac{4211}{5130}\right)
χ731025(7,⋅)\chi_{731025}(7,\cdot) 731025.bpn 2052 no −1-1 11 e(20212052)e\left(\frac{2021}{2052}\right) e(9951026)e\left(\frac{995}{1026}\right) e(16012052)e\left(\frac{1601}{2052}\right) e(653684)e\left(\frac{653}{684}\right) e(302513)e\left(\frac{302}{513}\right) e(8592052)e\left(\frac{859}{2052}\right) e(7851026)e\left(\frac{785}{1026}\right) e(482513)e\left(\frac{482}{513}\right) e(103684)e\left(\frac{103}{684}\right) e(11772052)e\left(\frac{1177}{2052}\right)
χ731025(8,⋅)\chi_{731025}(8,\cdot) 731025.bri 3420 no −1-1 11 e(7333420)e\left(\frac{733}{3420}\right) e(7331710)e\left(\frac{733}{1710}\right) e(653684)e\left(\frac{653}{684}\right) e(7331140)e\left(\frac{733}{1140}\right) e(291710)e\left(\frac{29}{1710}\right) e(6173420)e\left(\frac{617}{3420}\right) e(2891710)e\left(\frac{289}{1710}\right) e(733855)e\left(\frac{733}{855}\right) e(291380)e\left(\frac{291}{380}\right) e(7913420)e\left(\frac{791}{3420}\right)
χ731025(11,⋅)\chi_{731025}(11,\cdot) 731025.btk 5130 yes −1-1 11 e(17395130)e\left(\frac{1739}{5130}\right) e(17392565)e\left(\frac{1739}{2565}\right) e(302513)e\left(\frac{302}{513}\right) e(291710)e\left(\frac{29}{1710}\right) e(17995130)e\left(\frac{1799}{5130}\right) e(6382565)e\left(\frac{638}{2565}\right) e(47595130)e\left(\frac{4759}{5130}\right) e(9132565)e\left(\frac{913}{2565}\right) e(12791710)e\left(\frac{1279}{1710}\right) e(17692565)e\left(\frac{1769}{2565}\right)
χ731025(13,⋅)\chi_{731025}(13,\cdot) 731025.buq 10260 yes 11 11 e(61710260)e\left(\frac{617}{10260}\right) e(6175130)e\left(\frac{617}{5130}\right) e(8592052)e\left(\frac{859}{2052}\right) e(6173420)e\left(\frac{617}{3420}\right) e(6382565)e\left(\frac{638}{2565}\right) e(748310260)e\left(\frac{7483}{10260}\right) e(12282565)e\left(\frac{1228}{2565}\right) e(6172565)e\left(\frac{617}{2565}\right) e(7391140)e\left(\frac{739}{1140}\right) e(316910260)e\left(\frac{3169}{10260}\right)
χ731025(14,⋅)\chi_{731025}(14,\cdot) 731025.bte 5130 yes 11 11 e(2895130)e\left(\frac{289}{5130}\right) e(2892565)e\left(\frac{289}{2565}\right) e(7851026)e\left(\frac{785}{1026}\right) e(2891710)e\left(\frac{289}{1710}\right) e(47595130)e\left(\frac{4759}{5130}\right) e(12282565)e\left(\frac{1228}{2565}\right) e(21072565)e\left(\frac{2107}{2565}\right) e(5782565)e\left(\frac{578}{2565}\right) e(62855)e\left(\frac{62}{855}\right) e(25242565)e\left(\frac{2524}{2565}\right)
χ731025(16,⋅)\chi_{731025}(16,\cdot) 731025.bqa 2565 yes 11 11 e(7332565)e\left(\frac{733}{2565}\right) e(14662565)e\left(\frac{1466}{2565}\right) e(482513)e\left(\frac{482}{513}\right) e(733855)e\left(\frac{733}{855}\right) e(9132565)e\left(\frac{913}{2565}\right) e(6172565)e\left(\frac{617}{2565}\right) e(5782565)e\left(\frac{578}{2565}\right) e(3672565)e\left(\frac{367}{2565}\right) e(196285)e\left(\frac{196}{285}\right) e(16462565)e\left(\frac{1646}{2565}\right)
χ731025(17,⋅)\chi_{731025}(17,\cdot) 731025.bsa 3420 no 11 11 e(10511140)e\left(\frac{1051}{1140}\right) e(481570)e\left(\frac{481}{570}\right) e(103684)e\left(\frac{103}{684}\right) e(291380)e\left(\frac{291}{380}\right) e(12791710)e\left(\frac{1279}{1710}\right) e(7391140)e\left(\frac{739}{1140}\right) e(62855)e\left(\frac{62}{855}\right) e(196285)e\left(\frac{196}{285}\right) e(32893420)e\left(\frac{3289}{3420}\right) e(22913420)e\left(\frac{2291}{3420}\right)
χ731025(22,⋅)\chi_{731025}(22,\cdot) 731025.bvj 10260 yes 11 11 e(421110260)e\left(\frac{4211}{10260}\right) e(42115130)e\left(\frac{4211}{5130}\right) e(11772052)e\left(\frac{1177}{2052}\right) e(7913420)e\left(\frac{791}{3420}\right) e(17692565)e\left(\frac{1769}{2565}\right) e(316910260)e\left(\frac{3169}{10260}\right) e(25242565)e\left(\frac{2524}{2565}\right) e(16462565)e\left(\frac{1646}{2565}\right) e(22913420)e\left(\frac{2291}{3420}\right) e(102710260)e\left(\frac{1027}{10260}\right)
χ731025(23,⋅)\chi_{731025}(23,\cdot) 731025.bvx 10260 yes 11 11 e(185310260)e\left(\frac{1853}{10260}\right) e(18535130)e\left(\frac{1853}{5130}\right) e(912052)e\left(\frac{91}{2052}\right) e(18533420)e\left(\frac{1853}{3420}\right) e(50895130)e\left(\frac{5089}{5130}\right) e(543710260)e\left(\frac{5437}{10260}\right) e(5772565)e\left(\frac{577}{2565}\right) e(18532565)e\left(\frac{1853}{2565}\right) e(4011140)e\left(\frac{401}{1140}\right) e(177110260)e\left(\frac{1771}{10260}\right)
χ731025(26,⋅)\chi_{731025}(26,\cdot) 731025.tr 114 no −1-1 11 e(538)e\left(\frac{5}{38}\right) e(519)e\left(\frac{5}{19}\right) e(2357)e\left(\frac{23}{57}\right) e(1538)e\left(\frac{15}{38}\right) e(67114)e\left(\frac{67}{114}\right) e(1519)e\left(\frac{15}{19}\right) e(61114)e\left(\frac{61}{114}\right) e(1019)e\left(\frac{10}{19}\right) e(65114)e\left(\frac{65}{114}\right) e(4157)e\left(\frac{41}{57}\right)
χ731025(28,⋅)\chi_{731025}(28,\cdot) 731025.wc 180 no −1-1 11 e(23180)e\left(\frac{23}{180}\right) e(2390)e\left(\frac{23}{90}\right) −i-i e(2360)e\left(\frac{23}{60}\right) e(415)e\left(\frac{4}{15}\right) e(97180)e\left(\frac{97}{180}\right) e(7990)e\left(\frac{79}{90}\right) e(2345)e\left(\frac{23}{45}\right) e(179180)e\left(\frac{179}{180}\right) e(71180)e\left(\frac{71}{180}\right)
χ731025(29,⋅)\chi_{731025}(29,\cdot) 731025.bsw 5130 yes 11 11 e(42835130)e\left(\frac{4283}{5130}\right) e(17182565)e\left(\frac{1718}{2565}\right) e(9431026)e\left(\frac{943}{1026}\right) e(8631710)e\left(\frac{863}{1710}\right) e(29635130)e\left(\frac{2963}{5130}\right) e(18862565)e\left(\frac{1886}{2565}\right) e(19342565)e\left(\frac{1934}{2565}\right) e(8712565)e\left(\frac{871}{2565}\right) e(124855)e\left(\frac{124}{855}\right) e(10582565)e\left(\frac{1058}{2565}\right)
χ731025(31,⋅)\chi_{731025}(31,\cdot) 731025.buc 5130 yes −1-1 11 e(33675130)e\left(\frac{3367}{5130}\right) e(8022565)e\left(\frac{802}{2565}\right) e(421513)e\left(\frac{421}{513}\right) e(16571710)e\left(\frac{1657}{1710}\right) e(14962565)e\left(\frac{1496}{2565}\right) e(2335130)e\left(\frac{233}{5130}\right) e(24475130)e\left(\frac{2447}{5130}\right) e(16042565)e\left(\frac{1604}{2565}\right) e(556855)e\left(\frac{556}{855}\right) e(12295130)e\left(\frac{1229}{5130}\right)
χ731025(32,⋅)\chi_{731025}(32,\cdot) 731025.bpx 2052 no −1-1 11 e(7332052)e\left(\frac{733}{2052}\right) e(7331026)e\left(\frac{733}{1026}\right) e(18972052)e\left(\frac{1897}{2052}\right) e(49684)e\left(\frac{49}{684}\right) e(7131026)e\left(\frac{713}{1026}\right) e(6172052)e\left(\frac{617}{2052}\right) e(2891026)e\left(\frac{289}{1026}\right) e(220513)e\left(\frac{220}{513}\right) e(139228)e\left(\frac{139}{228}\right) e(1072052)e\left(\frac{107}{2052}\right)
χ731025(34,⋅)\chi_{731025}(34,\cdot) 731025.bua 5130 yes −1-1 11 e(25482565)e\left(\frac{2548}{2565}\right) e(25312565)e\left(\frac{2531}{2565}\right) e(1391026)e\left(\frac{139}{1026}\right) e(838855)e\left(\frac{838}{855}\right) e(2232565)e\left(\frac{223}{2565}\right) e(18172565)e\left(\frac{1817}{2565}\right) e(6615130)e\left(\frac{661}{5130}\right) e(24972565)e\left(\frac{2497}{2565}\right) e(15111710)e\left(\frac{1511}{1710}\right) e(2062565)e\left(\frac{206}{2565}\right)
χ731025(37,⋅)\chi_{731025}(37,\cdot) 731025.bre 3420 no 11 11 e(12293420)e\left(\frac{1229}{3420}\right) e(12291710)e\left(\frac{1229}{1710}\right) e(295684)e\left(\frac{295}{684}\right) e(891140)e\left(\frac{89}{1140}\right) e(626855)e\left(\frac{626}{855}\right) e(2113420)e\left(\frac{211}{3420}\right) e(676855)e\left(\frac{676}{855}\right) e(374855)e\left(\frac{374}{855}\right) e(2891140)e\left(\frac{289}{1140}\right) e(3133420)e\left(\frac{313}{3420}\right)
χ731025(41,⋅)\chi_{731025}(41,\cdot) 731025.bsz 5130 yes 11 11 e(9682565)e\left(\frac{968}{2565}\right) e(19362565)e\left(\frac{1936}{2565}\right) e(46513)e\left(\frac{46}{513}\right) e(113855)e\left(\frac{113}{855}\right) e(48315130)e\left(\frac{4831}{5130}\right) e(5395130)e\left(\frac{539}{5130}\right) e(11982565)e\left(\frac{1198}{2565}\right) e(13072565)e\left(\frac{1307}{2565}\right) e(4511710)e\left(\frac{451}{1710}\right) e(16375130)e\left(\frac{1637}{5130}\right)
χ731025(43,⋅)\chi_{731025}(43,\cdot) 731025.boq 2052 no −1-1 11 e(6352052)e\left(\frac{635}{2052}\right) e(6351026)e\left(\frac{635}{1026}\right) e(1552052)e\left(\frac{155}{2052}\right) e(635684)e\left(\frac{635}{684}\right) e(413513)e\left(\frac{413}{513}\right) e(10932052)e\left(\frac{1093}{2052}\right) e(3951026)e\left(\frac{395}{1026}\right) e(122513)e\left(\frac{122}{513}\right) e(127228)e\left(\frac{127}{228}\right) e(2352052)e\left(\frac{235}{2052}\right)
χ731025(44,⋅)\chi_{731025}(44,\cdot) 731025.bms 1710 no −1-1 11 e(412855)e\left(\frac{412}{855}\right) e(824855)e\left(\frac{824}{855}\right) e(191342)e\left(\frac{191}{342}\right) e(127285)e\left(\frac{127}{285}\right) e(491710)e\left(\frac{49}{1710}\right) e(6311710)e\left(\frac{631}{1710}\right) e(23570)e\left(\frac{23}{570}\right) e(793855)e\left(\frac{793}{855}\right) e(506855)e\left(\frac{506}{855}\right) e(97190)e\left(\frac{97}{190}\right)
χ731025(46,⋅)\chi_{731025}(46,\cdot) 731025.bnn 1710 no −1-1 11 e(4311710)e\left(\frac{431}{1710}\right) e(431855)e\left(\frac{431}{855}\right) e(5171)e\left(\frac{5}{171}\right) e(431570)e\left(\frac{431}{570}\right) e(283855)e\left(\frac{283}{855}\right) e(10091710)e\left(\frac{1009}{1710}\right) e(4811710)e\left(\frac{481}{1710}\right) e(7855)e\left(\frac{7}{855}\right) e(2695)e\left(\frac{26}{95}\right) e(9971710)e\left(\frac{997}{1710}\right)
χ731025(47,⋅)\chi_{731025}(47,\cdot) 731025.buz 10260 yes 11 11 e(57110260)e\left(\frac{571}{10260}\right) e(5715130)e\left(\frac{571}{5130}\right) e(14932052)e\left(\frac{1493}{2052}\right) e(5713420)e\left(\frac{571}{3420}\right) e(2035130)e\left(\frac{203}{5130}\right) e(203910260)e\left(\frac{2039}{10260}\right) e(20092565)e\left(\frac{2009}{2565}\right) e(5712565)e\left(\frac{571}{2565}\right) e(17413420)e\left(\frac{1741}{3420}\right) e(97710260)e\left(\frac{977}{10260}\right)
χ731025(49,⋅)\chi_{731025}(49,\cdot) 731025.bjt 1026 no 11 11 e(9951026)e\left(\frac{995}{1026}\right) e(482513)e\left(\frac{482}{513}\right) e(5751026)e\left(\frac{575}{1026}\right) e(311342)e\left(\frac{311}{342}\right) e(91513)e\left(\frac{91}{513}\right) e(8591026)e\left(\frac{859}{1026}\right) e(272513)e\left(\frac{272}{513}\right) e(451513)e\left(\frac{451}{513}\right) e(103342)e\left(\frac{103}{342}\right) e(1511026)e\left(\frac{151}{1026}\right)
χ731025(52,⋅)\chi_{731025}(52,\cdot) 731025.buu 10260 yes 11 11 e(208310260)e\left(\frac{2083}{10260}\right) e(20835130)e\left(\frac{2083}{5130}\right) e(7972052)e\left(\frac{797}{2052}\right) e(20833420)e\left(\frac{2083}{3420}\right) e(23772565)e\left(\frac{2377}{2565}\right) e(871710260)e\left(\frac{8717}{10260}\right) e(15172565)e\left(\frac{1517}{2565}\right) e(20832565)e\left(\frac{2083}{2565}\right) e(187380)e\left(\frac{187}{380}\right) e(133110260)e\left(\frac{1331}{10260}\right)
χ731025(53,⋅)\chi_{731025}(53,\cdot) 731025.bru 3420 no −1-1 11 e(14573420)e\left(\frac{1457}{3420}\right) e(14571710)e\left(\frac{1457}{1710}\right) e(3776)e\left(\frac{37}{76}\right) e(3171140)e\left(\frac{317}{1140}\right) e(107570)e\left(\frac{107}{570}\right) e(5533420)e\left(\frac{553}{3420}\right) e(15611710)e\left(\frac{1561}{1710}\right) e(602855)e\left(\frac{602}{855}\right) e(30713420)e\left(\frac{3071}{3420}\right) e(20993420)e\left(\frac{2099}{3420}\right)
χ731025(56,⋅)\chi_{731025}(56,\cdot) 731025.bth 5130 yes 11 11 e(5112565)e\left(\frac{511}{2565}\right) e(10222565)e\left(\frac{1022}{2565}\right) e(377513)e\left(\frac{377}{513}\right) e(511855)e\left(\frac{511}{855}\right) e(31075130)e\left(\frac{3107}{5130}\right) e(30735130)e\left(\frac{3073}{5130}\right) e(23962565)e\left(\frac{2396}{2565}\right) e(20442565)e\left(\frac{2044}{2565}\right) e(15671710)e\left(\frac{1567}{1710}\right) e(41295130)e\left(\frac{4129}{5130}\right)
χ731025(58,⋅)\chi_{731025}(58,\cdot) 731025.bvn 10260 yes −1-1 11 e(929910260)e\left(\frac{9299}{10260}\right) e(41695130)e\left(\frac{4169}{5130}\right) e(18552052)e\left(\frac{1855}{2052}\right) e(24593420)e\left(\frac{2459}{3420}\right) e(23512565)e\left(\frac{2351}{2565}\right) e(816110260)e\left(\frac{8161}{10260}\right) e(41575130)e\left(\frac{4157}{5130}\right) e(16042565)e\left(\frac{1604}{2565}\right) e(2293420)e\left(\frac{229}{3420}\right) e(844310260)e\left(\frac{8443}{10260}\right)
χ731025(59,⋅)\chi_{731025}(59,\cdot) 731025.bte 5130 yes 11 11 e(50715130)e\left(\frac{5071}{5130}\right) e(25062565)e\left(\frac{2506}{2565}\right) e(351026)e\left(\frac{35}{1026}\right) e(16511710)e\left(\frac{1651}{1710}\right) e(2715130)e\left(\frac{271}{5130}\right) e(12672565)e\left(\frac{1267}{2565}\right) e(582565)e\left(\frac{58}{2565}\right) e(24472565)e\left(\frac{2447}{2565}\right) e(653855)e\left(\frac{653}{855}\right) e(1062565)e\left(\frac{106}{2565}\right)
χ731025(61,⋅)\chi_{731025}(61,\cdot) 731025.bqf 2565 yes 11 11 e(822565)e\left(\frac{82}{2565}\right) e(1642565)e\left(\frac{164}{2565}\right) e(389513)e\left(\frac{389}{513}\right) e(82855)e\left(\frac{82}{855}\right) e(19422565)e\left(\frac{1942}{2565}\right) e(10432565)e\left(\frac{1043}{2565}\right) e(20272565)e\left(\frac{2027}{2565}\right) e(3282565)e\left(\frac{328}{2565}\right) e(832855)e\left(\frac{832}{855}\right) e(20242565)e\left(\frac{2024}{2565}\right)
χ731025(62,⋅)\chi_{731025}(62,\cdot) 731025.vw 180 no 11 11 e(131180)e\left(\frac{131}{180}\right) e(4190)e\left(\frac{41}{90}\right) e(2936)e\left(\frac{29}{36}\right) e(1160)e\left(\frac{11}{60}\right) e(8390)e\left(\frac{83}{90}\right) e(19180)e\left(\frac{19}{180}\right) e(815)e\left(\frac{8}{15}\right) e(4145)e\left(\frac{41}{45}\right) e(103180)e\left(\frac{103}{180}\right) e(1320)e\left(\frac{13}{20}\right)
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